Inverse Square root of a rectangular matrix

Question

I am trying to compute the inverse square root ($X^{-1/2}$) of a $n \times p$ matrix with $n > p$.

I was wondering if we can compute it via SVD just as we do it for square diagonalizable matrices i.e. $US^{-1/2}V$ etc.?

Or is there some other way of doing it?

I'd prefer a fast and efficient way as I have n=300,000 & p=50.

Thanks!

Answer 1

SVD will work for this, exactly as you expect. If your matrix is sparse, the Lanczos algorithm may be better.